P1112 Spring 2009 Homework #14 will not be collected. Solutions posted Friday May 1, and some of the HW will be covered in section. Reading: 13.3 – 13.8 (you may skip 13.4 molecules) Problems: 1. Y&F 11.72 Lifting a bicycle wheel over a curb. 2.Y&F 13.55Physical pendulum. 3.The position as a function of time t for a block of mass moscillating on a horizontal ideal spring of spring constant kis x(t) = Acos(ωt). (a) Write the oscillator's velocity v(t) and acceleration a(t) in the form Ccos(ωt+ φ), with C > 0, and find the constants Cand φfor each function. Your answers should be in terms of A,ω, and numerical constants. (b) Write the oscillator's kinetic energy K(t) and elastic potential energy U(t) as functions of time t that are linear in sine or cosine of t. Your answers should be in terms of A,ω, k, m, and numerical constants. [HINT: The following trig identities will be useful: sin2θ= (1 - cos2θ)/2 and cos2θ= (1 + cos2θ)/2.] (c) For two complete cyclesof this oscillation, draw graphs showing the oscillator's position x(t), velocity v
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